Most jobs in China require a degree, however you can still find work without. In answer to your specific questions:

1) Yes, you should take a course. Firstly this will help you get work since you don't yet have a degree. Secondly it will teach you something about TEFL itself so you're not floundering in the classroom. Thirdly it is a sign of respect for your students; I mean would you be happy knowing your teachers had no formal qualifications at all?

2) Your passport needs to be up to date and should not expire for at least 15 months after your gap year is up. You'll need a Z-visa also. Other paperwork can be organised once you're there. Many schools will help with these things.

3) Since this is (presumably) your first trip out there and since there is paperwork to be done and you're not fully qualified for most jobs, I'd recommend getting work before you get out there. Having said that, if it's not possible you could always jump on a plane and sort out work when you're there. You wouldn't be the first person to do that!!

You can do it two ways, either use an agency or find work yourself. A lot of people just go through the jobs online (and there are loads for China) and then start applying. If you start enquiring to a number of these you'll start to get a feel for the kind of jobs available, usual salaries and so on. You'll also get more choice as most agencies (in my experience) tend to stick to a single town or region.

Having said that, I'm sure there are posters on this forum who will be able to recommend agencies they've used.

I recommend using Teach Away Inc. This agency has offices in Toronto and Vancouver and many of our graduates have used it. As far as I know, they do not charge for job placement service and if so, then NEVER PAY FOR THIS SERVICE!!! Some TEFL schools charge over $1,000 for "hassle-free" job placement and claim to offer many benefits. Truth is... it is the English institute that hires you which provides the teacher with return airfare, free accommodation, work permit, etc... and one online school from the UK, which offers 4-month internships in China, was found to offer a salary way below the national average. If you're still looking for a reputable course, our 100-hour online course will provide you with the credentials to teach anywhere in Asia. www.ontesol.com

A degree is not a requirement for teaching in China, it's a requirement for obtaining a foreign experts certificate which is needed for a Z visa, sometimes called a work permit. Do not despair however, because it is possible to teach in China on tourist visas. I say visa's because at the moment you can get a maximum of two thirty day stays, so if you plan to be out here for more than two months, you're going to need to live within reasonable travelling distance of Hong Kong so you can renew your tourist visa as necessary. Having said that, working with only a tourist visa in China is illegal, and you risk being deported by doing so. Having said that, your employer will register you with the local police, and simply pay whoever needs paying to turn a blind eye to the fact you don't have a Z visa. In my time in China I've come across many people working on tourist visa's for a variety of reasons, and none of them have ever had a problem. I have posted on several TEFL forums asking if anyone has ever been deported, or had personal experience of someone else being deported, as opposed to 'a friend of a friend heard about someone', and out of dozens of replies and hundreds of viewings, only one person knew of anyone being deported, and that person had broken several other laws as well. So, and I'm sure a few people on the boards here will jump in and tell you never, ever to work on a tourist visa anywhere, you should think carefully, but in my opinion come over, you'll have the best year of your life so far if you come with an open mind.

Personally I don't see the point of going through an agency, when there are so many schools advertising directly on websites like Dave's ESL Cafe (Google it), which has new jobs advertised daily. I can personally recommend the http://www.tefl-bond.com/eng/home.php, who run two private shcools in Xiaolan and Shiqi in Zhongshan. Xiaolan is not a pretty town, but the people are very friendly and really make foreigners feel welcome and special. Shiqi is prettier, and has more western bars and restaurants. Zhuhai, further south, and on the border with Macau, is even prettier, and has even more expats and western style night-life. Personally, I didn't come to China to hang out with other foreigners all the time, but you don't have to, and it's nice sometimes to be able to relax and talk English with other westerners. They're all in easy travelling distance, a couple of hours at most, from Hong Kong. Also look at Guangzhou, and Shenzhen, both really big cities close to Hong Kong.

So, do the TEFL course, then get the job before you go. Check out Dave's ESL Cafe, and just search for teaching jobs in China. Even if an advert says degree required, email them and explain that you don't have one, but would like to teach anyway, and tell them your TEFL certified. Before you commit though, do a lot of research, both on schools, some of which can be horrendous, and teaching and living in China in general. China is not for everyone. The teaching is different from any other country you could teach in, and the culture can feel very alien at times. Learn some mandarin, even if it's only xie xie, or thank you before you come over, it will make a world of difference to your enjoyment. Check out http://middlekingdomlife.com/guide/ before you decide too, the most informative site for foreigners coming to China IMO.

A degree is not a requirement for teaching in China, it's a requirement for obtaining a foreign experts certificate which is needed for a Z visa, sometimes called a work permit

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A Z visa is different from a residence permit (there's no such things as a work permit). You need a degree to get a Foreign Expert’s Cert which enables you to get a RP. In the provinces working on Z visa (i.e. without a degree or FEC is fine).

In my time in China I've come across many people working on tourist visa's for a variety of reasons, and none of them have ever had a problem.

I’ve seen people fined and booted from the country. I’ve seen it happen in Shenzhen, Changsha and Fuzhou.